12.1 Revenue and Operating Drivers

Why Operational Modeling Is a Core FMVA Course

CFI's 2026 core list places Operational Modeling immediately after the three-statement sequence. The three-statement model in Chapter 10 already showed how net income, depreciation, capex, and ΔNWC must articulate. This chapter builds the schedules that produce those lines: a revenue and cost driver stack, a working-capital schedule, and a PP&E / depreciation schedule. Those three schedules are also the operating half of unlevered free cash flow (UFCF) used in DCF: UFCF = EBIT × (1 − t) + D&A − Capex − ΔNWC. If the drivers are slogans, the case study will not flex when the examiner changes volume, price, or days.

A driver-based operating model hardcodes a small set of assumptions (volume, price, mix, unit cost, fixed SG&A, variable SG&A percent, days, capex policy) and computes every income-statement line as a formula. A growth-rate model hardcodes a single revenue growth percent and a stack of percents of sales. Both appear on the FMVA final. The growth-rate method is faster. The volume × price method is what you use when the case gives units, when mix is shifting, or when you need to show operating leverage rather than a forced margin.

This chapter uses one company, Northstar Industrial, a packaging-components manufacturer. Year 0 is historical. Year 1 is the first forecast. Section 12.1 builds revenue and operating costs through EBIT. Section 12.2 converts the P&L into net working capital. Section 12.3 adds the $10 million capex project and the depreciation schedule. D&A in this section is the existing $6,000,000 charge so leverage is visible before the new asset lands.

Volume × Price Versus a Single Growth Rate

Revenue = volume × price. Forecast each piece, then multiply. Do not add the two growth rates and call the sum the revenue growth rate.

CFI's compact teaching identity — the one to memorize and then scale — is:

• Year 0: 1,000 units × $50 = $50,000
• Volume growth: 5% → 1,000 × 1.05 = 1,050 units
• Price growth: 3% → $50 × 1.03 = $51.50
• Year 1 revenue: 1,050 × $51.50 = $54,075

The growth-rate shortcut of 5% + 3% = 8% produces $50,000 × 1.08 = $54,000. The $75 gap is not a rounding error. It is the cross-term: new units also sell at the new price.

(1 + 0.05) × (1 + 0.03) − 1 = 8.15%, and 8.15% × $50,000 = $4,075, matching $54,075 − $50,000. Algebra: g_rev = g_vol + g_price + (g_vol × g_price).

Revenue bridge at 1,000 units

Northstar's live model is the same identity at 1,000,000 units: Year 0 revenue $50,000,000, Year 1 revenue $54,075,000. The missed cross-term becomes $75,000. On a 50-question timed exam that is not a rounding choice; it is a formula error that then flows into COGS, SG&A, AR, and UFCF.

When the case does not give units, a single g_rev is acceptable — that is how many compact three-statement cases are written. When the case does give units and price, do not collapse them. Interview-style items often ask why 3% price plus 5% volume is not 8% revenue growth. The answer is the 0.15% cross-term.

Mix and Segment Drivers

Blended average selling price (ASP) is an output of mix, not an independent input, once you have segments. Northstar has two products in Year 0:

Hold mix constant, apply 5% volume and 3% price to each segment:

• Standard: 840,000 × $41.20 = $34,608,000
• Premium: 210,000 × $92.70 = $19,467,000
• Total: $54,075,000 (same as the one-line identity)

Now shift mix: Year 1 still has 1,050,000 units, but premium rises from 20% to 24% of volume (252,000 premium; 798,000 standard), still with 3% price growth:

• Standard: 798,000 × $41.20 = $32,877,600
• Premium: 252,000 × $92.70 = $23,360,400
• Total: $56,238,000
• Blended ASP: $56,238,000 / 1,050,000 = $53.56

The mix effect versus constant-mix Year 1 is $56,238,000 − $54,075,000 = $2,163,000. That is not price inflation and not volume. A model that only has blended ASP + total units will hide it unless you change ASP by hand — and then you can no longer tell whether ASP moved because of list prices or because the sales force sold more premium. Exam trap: raising blended ASP 3% while also shifting mix toward premium double-counts the premium price.

Build one volume row and one price row per segment, then sum. Use SUMPRODUCT in Excel, not a single blended ASP that you then override.

Seasonality

An annual case can live with annual volume × annual price. A monthly or quarterly case, or any cash-flow discussion of a seasonal manufacturer, cannot. Northstar's Year 1 annual revenue of $54,075,000 is not earned 25% per quarter.

Equal-quarter modeling books $13,518,750 every quarter. That overstates Q1 by $3,785,250 and understates Q4 by $5,407,500. The annual total still tiles, so an annual three-statement model can look fine. Intra-year cash, the revolver peak, and year-end AR will not.

Year-end AR from the annual days method (section 12.2) is DSO × annual sales / 365. That implicitly assumes a flat daily run-rate. If Q4 is the peak and you instead take 45 trailing days of Q4 sales: Q4 daily sales ≈ $18,926,250 / 91 ≈ $208,000, and 45 × $208,000 ≈ $9,360,000 of AR — versus $6,666,781 from the annual formula. Compact FMVA cases still use the annual formula unless the prompt is monthly. Know which clock you are on.

COGS: Percent of Sales Versus Unit Cost

Two legal ways to forecast cost of goods sold (COGS):

1. COGS % of sales: COGS_t = COGS% × Revenue_t. Fast. Correct when the case gives no unit cost and gross margin is the driver.
2. Unit cost: COGS_t = Volume_t × Cost per unit_t. Correct when the case gives units, inflation, or a bill of materials.

Northstar Year 0 unit cost is $28.00, so COGS = 1,000,000 × $28 = $28,000,000 and COGS% = 28 / 50 = 56.0%. Year 1 input inflation is 2%, so unit cost = $28 × 1.02 = $28.56. Year 1 COGS = 1,050,000 × $28.56 = $29,988,000. Year 1 COGS% = 29,988,000 / 54,075,000 = 55.5%.

Gross margin rose from 44.0% to 44.5% with no heroic cost-cutting: price (+3%) outran unit cost (+2%). Holding COGS at 56% of Year 1 sales books COGS = 0.56 × $54,075,000 = $30,282,000, which is $294,000 too high and erases that real gross-margin lift.

Exam trap: tying COGS% to revenue after you have already modeled volume × unit cost. You then have two COGS figures. Same trap as forcing net margin in Chapter 10: one residual, not two.

If manufacturing overhead is partly fixed, split COGS the same way SG&A is split below (for example $4,000,000 factory overhead + $24 variable per unit). Year 0 still totals $28,000,000. Year 1 volume growth then leverages the fixed factory. This section keeps COGS fully variable at $28.56 so the SG&A split can carry the leverage lesson without two moving parts.

SG&A as Fixed Plus Variable

Selling, general, and administrative expense (SG&A) is rarely a pure percent of sales once you look inside it. Sales commissions and shipping flex with revenue. Rent, HQ payroll, insurance, and the audit fee do not — not in Year 1.

Northstar's split:

• Fixed SG&A: $6,000,000
• Variable SG&A: 8% of sales

Holding SG&A at 20% of Year 1 sales books $10,815,000, which is $489,000 too high. That error lands in EBIT, tax, net income, retained earnings, and UFCF. The 20% historical ratio is a check, not a Year 1 input, once you have a fixed-plus-variable structure.

Fixed SG&A does not stay frozen forever. A second plant, a new ERP, or a union step-up is a step-fixed cost: model it as a timed add-on, not as a silent percent of sales. For a one-year FMVA case, $6,000,000 plus 8% is the default.

Operating Leverage and Contribution Margin

Contribution margin is what remains after variable costs to cover fixed costs and then profit.

Northstar variable cost per unit at Year 0 prices:

• Unit COGS $28
• Variable SG&A $4 (8% × $50)
• Variable cost = $32 per unit
• Contribution = $50 − $32 = $18 per unit
• Contribution margin % = 18 / 50 = 36%
• Year 0 contribution dollars = 1,000,000 × $18 = $18,000,000

Fixed costs in the EBIT calculation: fixed SG&A $6,000,000 + D&A $6,000,000 = $12,000,000. Year 0 EBIT = 18,000,000 − 12,000,000 = $6,000,000.

Degree of operating leverage (DOL) at Year 0:

DOL = Contribution margin dollars / EBIT = $18,000,000 / $6,000,000 = 3.0x

Interpretation: a 1% change in volume, holding price and variable cost per unit constant, changes EBIT by 3%. Proof on a 5% volume increase with price still $50 and unit cost still $28:

Extra units × $18 contribution = 50,000 × $18 = $900,000. %ΔEBIT = 900,000 / 6,000,000 = 15%. %ΔSales = 5%. DOL = 15 / 5 = 3.0x. Fixed costs amplified the volume shock: revenue rose $2,500,000, but EBIT rose $900,000 — 36% of the extra revenue, which is exactly the contribution margin, because fixed costs did not move.

If you measure leverage before D&A (cash operating profit $12,000,000), DOL = 18 / 12 = 1.5x, and the same 5% volume shock raises that profit by 7.5% to $12,900,000. State the EBIT definition you are using. On the FMVA final, EBIT includes D&A unless the prompt says otherwise, so 3.0x is the Northstar figure.

Price changes are not what DOL measures. Year 1 with 5% volume, 3% price, and 2% unit-cost inflation produces a larger EBIT jump because the $1.50 price increase flows almost entirely to contribution (unit cost only rose $0.56):

EBIT grew 29.4% on 8.15% revenue growth. That is leverage plus a positive price-cost spread, not the pure 3.0x volume DOL. Section 12.3 will put a $10 million asset into service, raise D&A to $8,000,000, and cut Year 1 EBIT to $5,761,000. The operating schedules and the capex schedule have to meet; you cannot freeze D&A as 12% of sales and still claim this P&L.

Exam Traps on Revenue and Operating Drivers

• Adding growth rates. 3% + 5% is not 8.15%. Multiply (1 + g_vol) × (1 + g_price).
• Blended ASP plus a mix shift. Pick one architecture: segments, or a single ASP. Not both independently.
• COGS% after unit cost is already in the model. Year 1 COGS is $29,988,000, not $30,282,000.
• SG&A% after a fixed-plus-variable split is already in the model. Year 1 SG&A is $10,326,000, not $10,815,000.
• Calling every margin movement "operating leverage." DOL is a volume elasticity of EBIT. Price/mix/cost inflation are separate bridges.
• Hardcoding Year 1 dollars. If the case changes volume from 5% to 6%, units, revenue, COGS, variable SG&A, contribution, and AR must all move. That is the point of a driver model feeding the three statements and DCF.